* Corresponding Author(s): mshishehsaz@scu.sc.ir

JCAMECH Vol. 49, No. 2, December 2018, pp 415-429

DOI: 10.22059/jcamech.2018.269612.342

A review on stress distribution, strength and failure of bolted

composite joints

Mohammad Shishesaz * and Mohammad Hosseini

Department of Mechanical engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

1. Introduction

In past decades, bolted joints have been extensively used as a

mean for joining parts together. Parts can be joined by different

means forming a single or a double lap joint or other possible forms

[1]. Based on the different materials used for the adherends,

numerous analytical models have been proposed in bolted or hybrid

joints (a combination of bolt/rivet and adhesive) to predict the joint

strength and/or failure. The results would help one to have a better

understanding on stress distribution in the joint while using a suitable

joint for any specific action. Bolted and riveted joints are subjected

to two basic types of stresses; shear and bearing stresses. The stress

distribution can be obtained either by a three dimensional or two-

dimensional finite element analysis, whichever is suitable, or by a

closed-form solution, if applicable. The method which is most

attractive to an engineer is to set up a series of differential equations

to describe the state of stress and strain in a unit width of the joint.

The governed differential equations which are based on the selected

material behavior of the selected model can be solved analytically,

or numerically when a closed-form solution is out of reach.

Sometimes, finite element procedure may be adopted to seek the

solution. Consequently, the design engineer is confronted with a long

list of models and may face a difficulty in finding the most

appropriate one for a particular application. The objective of this

work is to review the analytical and numerical models, based on the

material behavior and type of joint type, to provide a guideline for

selection of proper model for prediction of stress distribution and/or

failure of the bolted or hybrid joints.

Typically, bolted or riveted joints can be divided into the

AR TIC LE IN FO AB S TR AC T

Article history:

Received: 2 November 2018

Accepted: 12 December 2018

In this study, analytical models considering different material and geometry for both single and double-lap bolted joints were reviewed for better understand how to select the proper model for a particular application. The survey indicates that the analytic models selected for the adhesively single or double bolted lap joints, as well as T, scarf, and stepped joints, with linear material properties are mostly two dimensional and the studies on stress distribution and/or failure of the joint are performed either experimentally, analytically or by finite element method. The results seem to be generally accurate and adequate. Additionally, it was shown that any increase in the bolt-hole clearance leads to an increase in bolt rotation, as well as a decrease in bolt-hole contact area, and hence, a reduction in joint stiffness. Moreover, studies on hybrid joints have revealed that the proper choice of adhesive material in conjunction with bolts or rivets in a joint, allows for significant increase in the static and fatigue strength compared to similar pure bonded joints. Additionally, the results on hybrid scarf joints showed that it is vital to place fasteners closer to the ends of the overlap to suppress the peak peeling stresses and hence, delay the effects of early crack initiation in the adhesive layer. Experimental studies on fatigue behavior and strength of bolted joints have shown that compared to clearance fit specimens, clamping force increases the fatigue life of a bolted joint. Moreover, higher tightening torque, in general, results in higher fatigue lives in bolted joints.

Keywords:

Plated bolted joints

Nonlinear behavior

Design, fatigue strength and failure

M. Shishesaz and M. Hosseini

416

following basic types shown in Fig. 1, although some other structural

joint configurations may be possible.

Figure 1: Some basic bolted and pin joints

Stress distribution in the bolted/riveted or hybrid joints depends

on the joint geometry and mechanical properties of the adhesive and

adherends. Among the main parameters affecting the stress field in

the joint one may point to the gripping force, number of bolts/rivets,

adherend thicknesses and properties, and stress-strain relations in the

adherend layers and properties of the adhesive in hybrid joints.

Different models, based on different material behaviors and

geometries have been proposed to investigate the displacement and

stress fields produced in the joint as a result of a tensile and/or shear

loads, as well as torsional and bending moments. In the sequel, these

analyses are subdivided into a few groups to mainly study the stress

distribution as well as failure of analyses of these joints.

2. Stress analysis in composite bolted/riveted joints

References [2-13] cover the pin or bolt effect on stress

distribution in composite joints. Reference [2] investigates the effect

of fiber arrangements on stress distribution around a pin in a

laminated composite joint. In this reference, it was assumed that all

fibers lie in one direction while loaded by a force Po at infinity (see

Fig. 2). Square and hexagonal arrangements of fibers were postulated

in the models. However, in Ref. [3], experiments and finite element

simulation were used to investigate the influence of geometric

parameters on stress distribution and failure response of bolted

single-lap composite joints. The stacking sequence of the laminate

was considered to be [0/0/+45/-45/0/90/0/+45/-45/0]s. Excellent

agreement between the experimental and finite element results was

observed. In addition, finite element method was applied to perform

the studies in Refs. and [3] and [5] as well as Refs. [6] and [8].

Reference [6] examines the three-dimensional contact stress in a

double lap joint (for carbon fiber reinforced plastic). The initially

selected stacking sequence was [45/0/-45/90]s. Moreover, in Ref. [8],

A preliminary numerical and experimental investigation of shear

stress distribution in multi-row bolted FRP joints was performed

using Finite element technique. Similar work on stress distribution

in bolted double-lap joints using 3-D finite element analysis was

performed in Ref. [9]. The numerical results were compared with

available closed-form equations. It was found that the results based

on 3-D finite element model were more reliable than simplistic 2-D

closed form solution. The effects of bolt-hole clearance on

mechanical behavior of bolted composite (graphite/epoxy) joints

were studied.

Figure 2: Composite pin joint subjected to tensile load [2].

The response of a bolted joint subjected to preload as well as

loaded in bending and torsion was studied by Hissam and Bower [9]

and Cavatorta et al. [11]. They used finite element modelling to

extract their results which were supported by experimental

observations. The selected material was a hybrid glass-carbon non-

woven fabric in epoxy matrix. The manufacturing technology was

hand lay-up with vacuum bagging. In another study, Ref. [14], the

two-dimensional semi-analytical solution method for stress analysis

of bolted composite lap joints under general in-plane loading was

found by Barut et al.. In Ref. [14], metal to composite bolted joint

behavior, evaluated at impact rates of loading, was investigated by

VanderKlok et al. They tested 4142 alloy steel-E glass ply epoxy

resin composite bolted joint under impact load, using a split

Hopkinson tension bar. They found that as the joint overlap length

increases, an asymptotic region of maximum bearing strength is

attained. In a numerical and experimental work by Camanho et al.

[15], the strength and efficiency of single-shear composite bolted

joints were explored. The single bolt was surrounded by a metallic

insert followed by the epoxy adhesive which was used to bond the

inserts into the composite laminate. The tensile properties of the

adhesive layer were determined using ASTM D683-72 standard. The

proposed model was able to predict the stress redistribution in the

joint as well as yielding of the adhesive layer.

Stress distribution in bolted joints has been also investigated by

other authors (Refs. [16-31]). Reference [16] presents an overview

on the behavior and analysis of bolted connections and joints in

pultruded fiber reinforced polymers. In Ref. [17], McCarthy and

Gray developed an analytical approach for modelling the load

distribution in multi-bolt composite joints. The bolts and laminates

were represented by a series of springs and masses where the effect

of static friction between laminates was taken into account. The

method was validated against experimental results (where possible)

and three-dimensional finite element models. The joint geometries

included single-bolt, single-lap joint as well as a three-bolt, single-

lap joint. Additionally, load sharing in single-lap bonded/bolted

composite joints was studied by Bodjona et al. and Bodjona and

Lessard in Refs. [18] and [19] respectively. A combination of a

bonded and bolted joint was used to result in a joint that was stronger

and more durable than either constituent separately. The objective of

the sensitivity analysis was to quantify the relative importance of the

different joint design parameters (factors) in load sharing. It was

shown that adhesive yield strength was mainly the most important

factor, while other factors, namely the joint E/D ratio, adhesive

thickness, and adhesive hardening slope were found to be other

significant factors influencing load sharing (D was the bolt diameter

and E represented the distance between free end of the substrate to

bolt centerline). A similar analysis on improving the load sharing in

hybrid bonded/bolted composite joints using an interference-fit bolt

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

417

was performed by Raju et al. [20]. In a related study, Mara et al. in

Ref. [21] investigated the performance improvement of the bolted

joints in fiber reinforced composite structures using metal inserts.

Their study showed that the bolt tension relaxation was minimized

and the joint efficiency was increased in terms of joint stiffness and

strength.

A simplified stress analysis of hybrid (bolted/bonded) joints was

performed by Paroissien et al. in Ref. [22]. Their investigation

allowed for the analysis of hybrid (bolted/bonded) joints made of

dissimilar laminated or monolithic adherends, as well as the

introduction of non-linear material behavior for both the adhesive

layer and the fasteners. It was shown that the proper choice of

adhesive material allows for significant increase in static and fatigue

strength compared to similar a pure bolted or bonded joint. In a

separate study, Taheri-Behrooz (Ref. [23]) investigated the effects of

material nonlinearity on load distribution in multi-bolt composite

joints. It was shown that increasing the degree of material

nonlinearity of the members causes a decrease and an increase in the

amount of the load transferred by the inner and outer bolts of the

joint, respectively. The effect of temperature on composite bolted

joints for aeronautical applications was discussed by Santiuste et al.

in Ref. [24]. A numerical model based on finite element method was

developed to evaluate the stresses in the bolt and composite plates.

The objective of the article was to avoid damage due to the cross-

effect of temperature and the torque when designing the composite

bolted joint. Results showed the significant effect of temperature

combined with torque level on the joint behavior. In a separate study

by Olmedo et al., an analytical model was developed to study the

secondary bending prediction in single-lap composite bolted joints

in Ref. [25]. Their model was validated through comparison of the

predicted load-displacement curve with the literature data as well as

the conducted experimental tests. A parametric study was also

performed to analyze the influence of main joint parameters on the

load-displacement curve. An experimental investigation on the

behavior of single lap composite bolted joint under traction loading

was performed in Ref. [26]. The experiments were designed to

identify the effects of stacking sequence of the layers, bolt diameter,

and loading rate on the joint the properties.

Reference [27] discusses the influence of lateral displacement of

the grip on the behavior of single lap composite-to-aluminum bolted

joints, via a novel model, using the finite element method. Tensile

tests on the joint were also conducted, while the lateral displacement

of the grip as well as the tensile displacement, out-of-plane

displacement, and surface strains were measured. The novel model

predicted 13 % smaller joint stiffness than the traditional model,

causing a delay in failure load of the joint due to lateral displacement

of the grip. In the study performed by Kratochvil and Becker [28],

the structural behavior of composite bolted joints was analyzed

using the complex potential method. In this work, the problem of a

pin-loaded hole in a symmetric composite plate was considered using

classical laminate theory. The analysis was performed using the

Lekhnitskii complex potential method. Their approach presented an

efficient method for the calculation of displacements and stresses in

the neighborhood of the hole where failure is likely to occur.

Evaluation of opening-hole shapes for rivet connection of a

composite plate, as well as fastener effects on mechanical behaviors

of double-lap composite joints and the effect of end geometry and

pin-hole effects on axially loaded adhesively bonded composite

joints were discussed in Refs. [29-31]. In Ref. [29], a comparative

evaluation was presented to analyze the influence of opening-

circular, elliptical, and racetrack hole shapes on structural stress

concentration in a composite plate. The finite element (FE) models

of the specimens with the three shapes for the rivet holes were

constructed. The stress distributions in finite element models under

tensile loading were analyzed to compare the stress concentration

factor for the foregoing hole shapes. It was found that the elliptical

and racetrack-shaped holes, produce smaller stress concentration

compared to the circular hole. A picture showing the three hole

shapes is shown in Fig. 3. However, the experimental and numerical

studies performed in Ref. [30] revealed the effect different fasteners

on mechanical behaviors of composite bolted joints. Experimental

tests were performed to depict the differences in the joint strength,

stiffness and failure mode between protruding head joint and

countersink joints. A similar study on the effects of pin hole

geometry, adherend thickness and joint type, on the joint behavior

was examined in Ref. [31]. Results showed that increasing the

sample thickness improves the joint performance in composite single

lap joints as well as in scarf joints. Additionally, the taper in single

lap joints provided a significant advantage over the simple single lap

joints, in terms of axial tensile strength.

Figure 3: A picture of the three hole shapes used in Ref. [30].

References [14, 32-35] study the composite bolted joint behavior

subjected to dynamic loads. In Ref. [32], the response of bolted

carbon fiber composite joints (and structures) subjected to constant

dynamic loading rates between 0.1 m/s and 10 m/s was studied. The

experimental results showed that the tested joints exhibit only minor

loading rate dependence when loaded in the pull-through direction

but when loaded in bearing at or above 1 m/s, there was a significant

change in failure mode. However, below a loading rate of 1 m/s, the

failure mode consisted of initial bolt bearing followed by bolt failure.

Additionally, for a loading rate of 1 m/s and above, the bolt failed in

a tearing mode. A similar study on the dynamic behavior of bolted

joints under heavy loadings was performed by Daouk et al. in Ref.

[33]. They designed a dynamic test bed, based on a bolted structure,

and performed the modal tests. The configuration of the bolted joint

and the level of the loading were the relevant parameters that were

considered in this study. Pearce et al. (Ref. [34]) proposed a stacked-

shell finite element approach for modelling the dynamically loaded

composite bolted joints under in-plane bearing loads. The onset of

failure modes, damage and the ultimate load of the joint were able to

be predicted by the models. In a separate study by VanderKlok et

al., Ref. [14], on the behavior of metal to composite bolted joints

under impact loading rates, quasi-static measurements were

conducted to distinguish the operational modes of failure as well as

the maximum bearing strength, corresponding to different edge

distance to hole diameter (e/d) ratios. Such joints form an integral

part of a majority of structural components used in aircraft and

automobile industries, where they can be subjected to either static or

time-dependent loadings. Results showed that the dynamic response

of a metal-composite bolted joint was significantly higher than its

static counterpart. Additionally, the asymptotic region of failure

mode alteration was observed to be dependent on loading rate

transfer in the joint. Reference [35] investigates the stress

distribution in multi-bolted joints for FRP pultruded composite

M. Shishesaz and M. Hosseini

418

structures. Distribution of shear stresses among different bolts by

varying the number of rows of bolts as well as the number of bolts

per row was examined. The effect of any change in washer diameter

on bearing stresses was also included in the analysis. According to

the results of this study, in multi-bolt joints, the load was not

distributed equally due to varying bolt position, bolt-torque or

tightening of the bolt, bolt-hole clearance, and friction at washer-

plate interface. A side view of the joint geometries used in Ref. [35]

is shown in Fig. 4. A similar experimental and simulation continuous

twice-impacts analysis of Ultra-High Molecule Weight Polyethylene

laminate which was fixed by four bolted joints was performed in Ref.

[36]. The experimental results of the first impact test were used to

verify the numerical model, in which a solid blunt projectile

penetrated the laminate with a velocity of 216 m/s.

Figure 4: Side view of the bolt arrangements used in ref. [35].

Experimental and numerical studies, as well as new designs on

laminated composite joints were discussed in Refs. [37, 38].

Additional studies on static and dynamic behavior of composite

riveted joints in tension as well as static and dynamic torque

characteristics of composite co-cured single lap joints were

discussed in Refs. [39, 40]. In Ref. [39], seven joint configurations

for aircraft application were tested based on three types of loading

conditions. The joint specimens were made of carbon fiber

reinforced plastic in a number of lay-ups of unidirectional tapes and

woven fabrics. It was shown that the effect of tensile loading rate on

variation of tensile strength is negligible for the tested composite

riveted joint specimens.

In addition to some of the previously mentioned studies, Refs.

[41-46] adopt finite element method to investigate the behavior of

bolted joints. Stocchi et al. (Ref. [41]), performed a detailed finite

element investigation on single lap composite bolted joints with

countersunk fasteners under static load. In their study, in addition to

the analysis of contact evolution between the bolts and the holes,

stress distribution in carbon fiber reinforced plastic plate and

titanium bolts were discussed, while the numerical results were

compared to experimental data. Five different stages were identified

in the joint behavior: (i) No-Slip, (ii) Slip, (iii) Full Contact, (iv)

Damage and (v) Final Failure. According to the results of their study,

the joint stiffness is higher in the No-Slip stage than in the Full

Contact stage. This was independent of coefficient of friction and

bolt clamping force. In Ref. [42], a simple homogenization scheme

for 3D finite element analysis of composite bolted joints was

presented by Mandal and Chakrabarti to determine the basic

mechanical behaviors of a laminated composite joint with

significantly lesser computational effort. To takes into account the

effect of transverse shear deformation in composite laminates, their

formulation was based on Mindlin–Reissner plate theory. Their

method was able to find equivalent homogeneous model for

laminated composite joints having any type of lamination scheme.

Reference [43] introduces the finite element modelling of blind

bolted composite joints. In this study, a detailed three-dimensional

finite element model was developed to study the behavior of blind

bolted endplate composite joints that connect composite beams to a

concrete-filled steel tubular column. Each part of the study was

modeled using proper element. The parametric studies were also

carried out to investigate the effects of shear studs and reinforcement

ratio, as well as column sections and thickness ratios, as well as blind

bolt types and diameters on the joint performance.

Experimental and finite element studies on bolted, bonded and

hybrid step lap joints of thick carbon fiber/epoxy panels which are

used in aircraft structures showed that the finite element models are

well capable of predicting the bonded, bolted and hybrid joint

strengths with a high accuracy [44]. According to the results based

on strain energy release rate, it is vital to place fasteners closer to the

ends of the overlap to suppress the peak peeling stresses and hence,

delay the effects of early crack initiation. A schematic diagram of the

hybrid joint is shown in Fig. 5.

Figure 5: A diagram of the hybrid step joint used in Ref. [44].

A similar experimental and finite element analysis of glass fiber

reinforced plastic composite laminates with combined bolted and

bonded joints is performed in Ref. [45]. A highly efficient user-

defined finite element for load distribution analysis of large-scale

bolted composite structures was developed by Gray and McCarthy

[46]. The method was a combination of analytical/numerical

approach and was capable of representing the full non-linear load-

displacement behavior of the bolted composite joints up to and

including, joint failure. A related study by the same authors on a

global bolted joint model for load distributions in multi-bolt

composite joints based on finite element analysis was presented in

Ref. [47]. They stated that their new model was found to be robust,

highly efficient and accurate, with time savings of up to 97% over

the full three-dimensional finite element models.

References [48-51] concentrate on the design of bolted and/or

hybrid joints. In Ref. [48], Zhou et al. proposed a novel design of

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

419

out-of-plane π joints to increase the load carrying capacity of the

joint. This type of joint uses bolts to connect the joint to other

structural components. Static experiments performed on the novel

bolted composite π joint and an aluminum counterpart showed that

the bolted carbon/epoxy composite π joint exhibits a larger load

carrying capability with a massive weight reduction compared to its

aluminum counterpart. Additionally, based on the numerical

simulation, the progressive damage process and failure mechanism

of the bolted composite π joint showed that the novel design not only

enhances the positive factors of composite and substantially

strengthens the composite π joint, but also it eliminates the potential

weaknesses in deltoid fillers. A schematic diagram of the π joint is

shown in Fig. 6.

In a related study by Cheng et al. [49], a novel design scheme

was proposed which mainly improved the layup design in the

composite bolted π-joint. In Ref. [50], the effects of several factors

on the strength of hybrid joints were examined using the Design of

Experiments methodology. The studied factors included adhesive

modulus, adhesive thickness, adherend thickness, bolt-hole

clearance and clamping area. It was found that the hybrid joints were

stronger than the bolted or bonded joints, and they have a better crack

arrest capability due to the hybridization effect. More investigations

on bolted and hybrid joints can be found in Ref. [51]. Three-

dimensional stress analysis of bolted single-lap composite joints was

investigated in Ref. [52] using a three-dimensional finite element

model which was developed to determine non-uniform stress

distributions through the thickness of composite laminates in the

vicinity of a bolt hole.

Figure 6: Schematic diagram of a π- joint used in Ref. [48].

3. Strength analysis of composite bolted/riveted joints

References [53-62] deal with strength analysis of bolted/pinned

(riveted) joints. In Ref. [53], a parametric finite element analysis was

performed to investigate the effect of the material property

degradation rules and failure criteria on the tensile behavior and

strength of bolted joints in a single-lap single-bolt graphite/epoxy

composite laminate. The predicted load-displacement curves and

failure loads were compared with experimental results for different

laminate stacking sequences and joint geometries. The authors

proposed a combination of failure criteria and material property

degradation rules that led to an accurate strength prediction of the

joint. The numerical results obtained on deformations, strains, and

bolt loads were validated with experimental findings. In another

study, bearing strength and failure behavior of bolted composite

joints was investigated by Yi Xiao and Takashi Ishikawa in Refs.

[54, 55]. To evaluate the effect of resin properties on bearing

response, two different types of polymer–matrix-based Carbon Fiber

Reinforced Plastic laminates were selected. In the first stage, their

experimental observations showed that the bearing failure can be

outlined as a process of compressive damage accumulation, which

can be divided into the following four stages: damage onset; damage

growth; local fracture; and finally, structural fracture. In the second

stage, an analytical model was developed to simulate the bearing

failure and response characteristics of each bolted composite joint.

Their proposed model accounted for the contact conditions at the

pin/hole interface, as well as the finite deformation, progressive

damage, and nonlinear behavior of the material.

An analytical model for strength prediction in multi-bolt

composite joints at various loading rates was proposed by Sharos et

al. in Ref. [56]. The analytical model was used to quickly determine

the complete load-displacement curve of single- and multi-fastener

composite joints. The loading rate effects, as well as bearing damage,

were included via a novel conic damage approximation function.

Their method was validated against experimental data.

In Part I of the study performed by McCarthy et al. (Ref. [57]), a

Three-dimensional finite element models were developed to study

the effects of bolt–hole clearance on the mechanical behavior of

single-bolt, single-lap graphite/epoxy composite joints. The

validated model was used in Part II of the study (Ref. [58]), to

investigate the effects of bolt–hole clearance on the joint stiffness,

stress state and failure initiation. It was shown that any increase in

the bolt-hole clearance leads to an increase in bolt rotation, as well

as a decrease in bolt-hole contact area, and hence, a reduction in joint

stiffness. The analytical model presented by Gray and McCarthy in

Ref. [59] for prediction of through-thickness stiffness in tension-

loaded composite bolted joints was the extension of a spring-based

method. Their proposed model accounted for the stiffness of the

clamped region of the joint due to bolt torque, as well as bolt

extension, flexural stiffness, and the anticlastic curvature within the

laminates. Three-dimensional finite element models of the bolted

composite plates were used to validate the method.

In the study performed by Zaroug et al. (Ref. [60]), experimental

and numerical investigation were used to seek the effects of adherend

material and thickness on the strength of bolted, bonded, and hybrid

single lap joints. In their study, the mechanical performance of

bonded, bolted, and hybrid single lap joints subjected to tensile

loading was examined using three different adherend thicknesses and

two different adherend materials with different mechanical

behaviors. Force-displacement curves, failure history, and the

amount of absorbed energy by each configuration were analyzed to

clarify the strength of various joints. In a separate study, Zhao et al.

in Ref. [61] used a probabilistic model to analyze the strength of a

double lap single-bolt composite joint. Static tensile tests were

performed on fifteen composite double lap single-bolt joints, made

of T800 carbon/epoxy composites. The probabilistic failure load of

the joint which was obtained from the proposed model was in good

agreement with the results of conducted experiments. It shows that

although the statistical parameters of the probabilistic failure loads

were slightly influenced by the probability distribution type of

random variables, the proposed model was not sensitive to this

distribution. Additional studies on strength analysis of composite

bolted joints can be found in Refs. [62-84].

4. Damage, fatigue and failure of bolted/riveted joint

Based on the nonlinear finite element approach, Nerilli and Vairo

[85] investigated the progressive damage of composite bolted joints.

In another study, the progressive bearing damage of composite

bolted joints under quasi-static shear loads was studied by Nezhad et

al. [86]. He and Ge [87] used a numerical scheme in the framework

of coupled continuum damage mechanics to predict failure of

composite multi-bolted joints. On the other hand, Zhou et al. [88]

proposed a three-dimensional finite element model for damage

M. Shishesaz and M. Hosseini

420

estimation of single-lap and multi-lap joints. Du et al. [89] used finite

element method to investigate the progressive damage of pultruded

fiber reinforced polymer bolted joints. In another study, Hühne et al.

[90] performed an investigation on the effect of liquid shim layers on

the progressive damage of composite bolted joints using finite

element method. A similar analysis on the progressive damage

analysis of multi-bolt composite joints in the framework of

characteristic length method was performed by Zhang et al. [91].

However, Kolks and Tserpes [92] suggested a progressive damage

model for predicting the mechanical behavior of titanium lamella in

a double-lap composite bolted joint subjected to tensile loading.

Chishti et al. [93] performed experimental tests for studying

progressive damage characteristics and strength of bolted joints of

composite laminates. Based on a continuum damage model, Zhou et

al. [94] introduced a damage model for double-lap and multi-bolt

composite joints under quasi-static loads. Additional studies on

damage analysis of composite bolted joints can be found in Refs. [95,

96].

The analytical and experimental studies performed by Awadhani

and Bewoor [97] reviled the effect of geometrical parameters such

as edge distance to diameter ratio or width to diameter ratio, on the

failure behavior of single-lap bolted joints between metal and GFRP

under axial tensile loads. Applying a tensile load on the single bolted

single lap joint, the failure modes were determined experimentally.

According to the results of this study, increasing the edge distance,

changed the failure mode form cleavage or net tension to bearing

failure. It was also concluded that the joint strength was increased

with an increase in edge distance. Hu et al. [98] used finite element

method to investigate the progressive failure in single-lap bolted

joints of woven fiber reinforced composites subject to high bearing

strains. Using explicit finite element analysis along with material

nonlinearity, the bearing failure characteristics of the bolted joint, as

well as the crushing of the composite material due to the rotation of

the bolt head were determined. The finite element results were in

agreement with experimental observations. Cheng et al. [99]

employed failure envelopment method and utilized the three-

dimensional finite element analysis to predict the failure behavior of

multi-bolt composite joints. Tensile experiments of two- and three-

bolt joints were conducted to obtain the failure modes and other joint

properties. Experimental findings were in agreement with 3D finite

element results. Warren et al. [100] introduced a three-dimensional

model in order to investigate progressive damage of single-bolt and

double-shear joints of woven composites. The modeled joint is

commonly used in many aerospace structures. The Hashin failure

criteria and the Matzenmiller-Lubliner-Taylor damage model as well

as the unique morphology of three-dimensional woven composites

were included in the study. The onset of damage the model were

found to be in agreement with previous experimental findings.

Bearing failure of Carbon-Epoxy composite bolted joints under

uniaxial and biaxial quasi-static loads was examined experimentally

by Kapidžić et al. [101]. In this work, uniaxial and biaxial quasi-

static bearing failure experiments were performed on carbon–epoxy

laminate specimens at elevated temperatures. The experiments were

also simulated by 3D, explicit, finite element analyses, which

included intralaminar damage and delamination. Results of the study

showed that the experimental and simulated bearing failure loads

differed by 1.7% in the uniaxial case and 2.1% in the biaxial case.

Liu et al. [102] performed a numerical analysis and experimental

study on bearing failure of single-lap composite joints with

countersunk. In this study, tensile experiments were conducted on

single-lap bolted joint with a countersunk fastener. Finite element

models were also prepared using cohesive elements to predict the

interlaminar damage in model I. In mode II, 8-node reduced

integration solid elements were selected to model all the parts with

3D Hashin-type initiation criteria and Camanho degradation law.

The results simulated by both models were able to accurately predict

the elastic loading response and the overall damage profile compared

with the experimental results. Based on the Huang’s criterion, Nerilli

et al. [103] modeled the progressive damage in multi-bolted joints

connecting structural elements made up of fiber-reinforced polymers

composite laminates. Differences in failure mode and values of

ultimate-load were numerically investigated. In the case of single-

bolted joints, the use of carbon-FRP laminates showed the best

mechanical properties. Ozen and Sayman [104] performed numerical

and experimental study on the failure behavior of pinned joints of

glass-fiber-reinforced composites containing two serial holes.

Experimental tests involved variations in a number of parameters

such as the distance between the center of two holes-to-hole

diameters (K/D), the edge distance-to- upper hole diameter (E/D),

and the width of the specimen-to-hole diameter (W/D). Results

showed that the immersion of test specimens into sea water causes a

decrease in failure load without a preload moment. Additionally, test

specimens under preload moments produced nearly the same bearing

strength as unimmersed specimens. Khashaba et al. [105, 106]

reported the effects of stacking sequences and of pin–hole clearance

on the failure behavior of pinned-joints composite laminates.

Theoretical models were developed to predict the characteristic

bearing strength, as well as lower bound bearing strength. Four

configurations for stacking sequences were studied: [0/90]2s,

[15/75]2s, [30/60]2s, and [45/45]2s. Results showed that specimens

with [0/90]2s stacking sequence had the ultimate failure stress and

maximum failure displacement compared with the other stacking

sequences. However, based on the first-peak criterion, specimens

with [45/45]2s stacking sequence showed the maximum failure

displacement and bearing capacity.

Wang et al. [107] utilized extended finite element method to

identify the progressive failure of bolted single-lap composite joints.

In their study, the extended finite element method (XFEM) was used

to predict the progressive failure of single-lap bolted joints. The

failure load in the joint, simulated by XFEM, was compared with the

experimental results in the literature. the influences of two geometric

parameters, namely plate width-to-hole diameter ratio (W/D) and the

edge-to-hole diameter ratio (E/D), on the failure load of single bolt

single-lap composite joint was also included in the study. In Ref.

[108], Liu et al. proposed a failure envelopment method (based on

the conventional failure envelope method presented by Hart-Smith)

to predict the final failure mode and strength of multi-bolt composite

joints. In a separate study, Soykok et al. [109] performed an

experimental analysis to investigate the effects of thermal

conduction and tightening torque on the failure of single lap double

serial fastener glass fiber-epoxy composite joints. It was observed

that, the load-carrying capacity of the joint gradually decreases by an

increase in temperature. The maximum decrease in failure loads

occurred at 70 oC and 80 oC due to the heat damage to the resin

matrix. Additionally, it was observed that the tightening torque

(which contributes to the joint strength) is effective not only at room

temperature, but also at elevated temperatures. A three-dimensional

method presented by Ataş et al. [110] for prediction of double lap

bolted joint strength in composite laminates showed that although

the in-plane failure mode of each individual layer in [0o/90o/±45o]2s

carbon fiber reinforced plastic laminates was predicted to happen

around the fastener hole, the X-ray radiographs indicated that

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

421

delamination failure is particularly dominant around the washer’s

outer edge. Lu et al. [111] suggested a three-directional explicit finite

element method for failure prediction of single-shear and double-

shear composite joints. A linear damage propagation law based on

the fracture energy and the characteristic length was adopted. The

predicted mechanical behavior was in good agreement with

experimental results.

Using experimental tests, Lee and Ahmad [112] studied the

effects of bearing stress, lay-up and plate aspect ratio on the failure

life of double-lap woven fabric kenaf fiber reinforced polymer

hybrid bonded-bolted joints. The effects of lay-up types, different

normalized plate width (plate width/hole diameter, W/d), and bolt

loads were incorporated into their study. The bearing stress at failure

increased with increments in W/d ratio. Zhao et al. [113] determined

stress concentration relief factor via tensile tests on open-, filled- and

loaded-hole laminates, failing in tensile mode, respectively. This

factor was used for determination of failure life in composite multi-

bolt joints. High-stress concentration level was found in loaded hole,

while the filled-hole had slightly higher stress concentration than that

of the open-hole. In another study, Zhang et al. [114] performed

numerical analysis and experimental tests to indicate the effects of

end distances on failure life of composite bolted joints. Using trial-

and-error method, a group of material degradation factors were

presented to establish the three-dimensional progressive damage

models of the bolted joints. According to the progressive damage

analyses, the predicted results on load-displacement curves, failure

patterns of bolted joints with different end distances, and failure

loads, were in good agreements with corresponding experimental

findings. Olmedo and Santiust [115] proposed a new set of failure

criteria to predict the composite failure in single-lap bolted-joints.

The advantage of their criteria with respect to the other three-

dimensional failure criteria was the consideration of non-linear shear

stress-strain relationship. In a separate work by Fun et al. [116],

bending behavior of a novel composite bolted π-joints was

investigated using experimental and numerical studies. The details

of their proposed novel -joint and its components are shown in the

non-scaled Fig. 7. The L and U-shaped preforms were made of quasi-

isotropic T300/6808 warp-knitting multi-layer fabrics while the base

preform was composed of composite plain cloth (G814/6084) with a

total thickness of 3 mm. The results of this study showed that

delamination of the fillet region in L-preform was the -joint's failure

mode. The hygrothermal effect on fatigue characteristics of jagged

pin-reinforced composite single-lap joints was studied by Ko et al.

[117]. Three environmental test conditions, namely, room

temperature and dry, elevated temperature and dry, and elevated

temperature and wet were considered. Results indicated that under

all test conditions, the joint strength was improved while reinforced

with the z-pins. However, when jagged z-pins were used under the

elevated temperatures and wet conditions, compared with the

corresponding values for an unpinned joint, the static and fatigue

strengths at a million cycles were increased by 32.2% and 65.8%,

respectively.

An experimental study was performed by Giannopoulos et al.

[118] to investigate the effects of bolt torque tightening on strength

and fatigue behavior of airframe FRP laminate bolted joints. Results

showed that for relatively heavily torqued pre-tightened joints,

failure took place mainly on the specimen part after the washer.

Based on the continuum damage mechanics, Sun et al. [119]

investigated the elastic-plastic fatigue and fretting fatigue

characteristics of double-lap bolted joints. Result showed that the

predicted fatigue lives agree well with the experimental results

(available in the literature). In a separate study, Scarselli et al. [120]

presented a model for prediction of failure loads in bolted laminated

composite joints subjected to cyclic loading.

Figure 7: A non-scaled picture of the novel π-joints (with its details) used in

Ref. [116].

Gathering the data through experimental activities, they proposed a

constitutive relationship between stress and strain. Using finite

element method in conjunction with Tsai-Hill criteria, Zhou et al.

[121] suggested a model for prediction of multi-axial fatigue

behavior of composite bolted joints. Their study adopted the

modified S-N fatigue life curve fitted by unidirectional laminate S-

N curve which takes the ply angle and stress ratio into consideration,

to determine fatigue life of composite bolted joint. Kapidžić et al.

[122] studied the effects of biaxial load and thermal loads on the

fatigue life of bolted joints. In their study, two-bolts, double-lap

joints with quasi-isotropic carbon–epoxy composite specimens were

subjected to uniaxial and biaxial cyclic loading at 90 oC. The

influence of biaxial load and bearing fatigue failure process were

investigated on the joint failure. Results showed that the biaxial

loading results in a longer fatigue life that the uniaxial loading.

Experimental and numerical study on the mechanical behavior of

blind bolted end plate joints as well as experimental tests for static

and dynamic failure behavior of bolted joints in carbon fiber

composites can be found in Refs. [123] and [124]. One can also find

additional work on failure of bolted/riveted joints in Refs. [97, 98,

112, 125-137] and [138-142].

In 1980, a strength review analysis of mechanically fastened

fiber reinforced plastic joints was presented by Godwin and

Matthews [143]. They discussed the effects of material, fasteners,

and design parameters in their report. In a related work, Agarwal

[144], studied the static strength prediction of bolted joints in

composite materials. He presented a new method for predicting the

strength of double-shear single-fastener composite joints. He used

finite element method to calculate the stress distribution around a

fastener hole, as well as predicting the various modes of laminate

failure through some modifications applied to the average stress

criterion. Choi et al. [65], studied the strength of a composite

laminated bolted joint subjected to a clamping force using the failure

area index method. Using this method, the strengths of different

geometric shapes and dimensions were predicted and compar[129]ed

with experimental results. It was shown that using failure area index

M. Shishesaz and M. Hosseini

422

method, the strength of a given laminated composite bolted joint

subjected to a clamping force can be predicted within a fairly

acceptable accuracy. In Ref. [145], Lin and Jen worked on failure

analysis of single-lapped bolted and bonded mixed-composite joints.

They performed numerical and experimental studies to generate their

data. Two kinds of stacking sequences in the adherends were tested:

quasi-isotropic and cross-ply. The adhesive layers included thermal-

setting and thermal-plastic types. Various multi-bolt and bonded

joints were made and tested. Two types of lay-ups were considered

for the adherends; cross-ply and the quasi-isotropic laminates. Three-

dimensional finite element analysis was used to obtain the stress and

strain fields within each specimen. Additionally, the C-scan

technique was adopted to determine the damage zone and failure

mechanism of the joint.

Other authors have also worked on the fatigue behavior,

development, damage and failure of composite bolted joints [146-

167]. Smith et al. [146], studied the behavior of single-lap bolted

joints in CFRP laminates. The strengths of single-lap bolted joints

were presented as functions of width and end distance in two carbon

fiber reinforced composite laminates. Comparing the results with

those of others, they showed that due to the joint bending effect, the

ultimate strength of a single-lap joint is lower than that of a double-

lap joint. On the other hand, experimental studies on fatigue behavior

and strength of bolted joints in Ref. [147] showed that compared to

clearance fit specimens, clamping force increases the fatigue life of

a bolted joint. According to Ref. [148], higher tightening torque, in

general, results in higher fatigue lives in bolted joints, Moreover, the

numerical simulation as well as experimental results showed that an

increase in clamping force, improves the fatigue life of double lap

bolted joints due to presence of compressive stresses around the hole.

Additionally, in Ref. [149], the effect of tightening torque as well as

the effect of plate thickness on the fatigue life of a single and double

lap joints were studied. The objective of the fatigue tests was to

demonstrate the failure trends for each material thickness, joint type,

and torque loading.

The development of fatigue damage around fastener holes in the

thick graphite/epoxy composite laminates was studied by Saunders

et al. [150]. Performing experiments on bolted composite laminates

subjected to fatigue loading, they discussed the mechanisms by

which the damaged area develops and eventually grows around

countersunk fastener holes. In Refs. [151] and [152], stresses

distribution around fasteners due to cheese-head and countersunk

bolts in composite structures in flexure, and their effect on fatigue

damage initiation was fully discussed. Comparison of the results on

experimental and theoretical models made it possible to predict the

location of fatigue damage initiation. In another study, using

nondestructive examination techniques, Persson et al. [153],

investigated the propagation of hole machining defects in the pin-

loaded carbon/epoxy laminates. They applied KTH-method (a

machining method which gives holes with no detectable defects

using non-destructive examination technique) and two other

traditional methods for machining holes. The samples were subjected

to uniaxial tension fatigue loading. Among their other results, they

concluded that the KTH specimens yielded the longest fatigue life.

An additional study on the effects of hole machining defects on the

strength and fatigue life of composite laminates was performed by

Persson et al. in Ref. [154]. In Ref. [155], the theory of micro-

mechanics of failure was extended to analyze the progressive fatigue

damage of carbon fiber reinforced polymer (CFRP) composites and

to predict the strength of bolted joint structures. Fatigue behavior of

mechanically fastened joints (bolted joints) was also discussed in

Refs. [156-160]. In these studies, the effects of protruding and

countersunk-bolt heads, as well as the quasi-isotropic and highly

orthotropic lay-ups and fastener systems, on the joint strength and

fatigue performance were studied. Fractographic SEM and optical

microscopy were used to explore the fracture and damage which was

developed in the joint system during static and fatigue testing.

Results showed a linear dependence between the number of bolt

rows and the fatigue life of the corresponding joints. Additionally,

the specimens joined by protruding-head bolts showed better static

and fatigue performance compared to the other joints bolted by

countersunk fasteners. According to the load-transfer calculations

results, different bolt rows transfer slightly different amounts of load.

According to the fractographic observation, the severe damage in the

bolted joints subjected to fatigue loading occurred around the bolt

holes. The experimental study of fatigue behavior of [0/90]4s double-

lap bolted joints was explored by Smith and Pascoe [161]. This study

also covered the effect of bolt clamp-up torque on fatigue behavior

of the laminate. The fatigue resistance of composite joints with

countersunk composite and metal fasteners, as well as protruding-

head bolts were also discussed in Refs. [162] and [163].

In Ref. [164], fatigue behavior of multiple-row bolted joints in

carbon/epoxy laminates was discussed by Persson and Eriksson. In

their study, the ranking order of factors affecting the strength and

fatigue life of multiple-row bolted composite laminates were

investigated. Eight different factors related to the geometry, material

properties, laminate configuration, hole quality, environmental

conditions, and fastener type were considered. Additionally, in the

studies performed in Refs. [165-167], the effect of secondary loads

on the common failure modes of composite aircraft structures,

fatigue characteristics of bolted joints for unidirectional composite

laminates, and the effect of repeated tensile loading on bearing

damage evolution of a pinned joint in CFRP laminates were

discussed, respectively.

Several other authors have also worked on the failure analysis of

composite bolted joints [107, 168-171]. In the study performed by

Wilson and Tsujimoto [168], they addressed the concepts used in

formulation of strength models and compared the capabilities of

some used failure criteria. According to their results, the differences

in predicted strengths based on the examined models were

insignificant. On the other hand, Wang et al. [169], extended the

finite element method to investigate the failure load prediction of

bolted single-lap composite joint. To investigate the effect of ply

angle on the failure response of a bolted composite single-lap joint,

a three-dimensional model was developed by Zhou et al. [170]. Their

model could predict the failure load and failure mode of the joint

with arbitrary ply angle. A related study similar to those outlined in

Refs. [169, 170] is performed in Ref. [107]. One can also find studies

on failure of bolted and riveted joints in Refs. [73, 171-173].

5. Conclusions

A literature review on the behavior of different bolted single and

double-lap joints (as well as others) has been made to assist a

designer to select the proper model for a particular application. The

survey shows that the analytic models selected for the bolted bonded

joints (single or double), as well as other types of joints (i.e. tee,

scarf, and stepped), with linear material properties are mostly two

dimensional where the solutions for stress distribution and/or failure

of the joint are investigated either experimentally or by finite element

method. The results seem to be generally accurate and adequate. A

combination of a bonded joint and bolted joint resulted in a joint that

was stronger and more durable than either constituent separately. It

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

423

was shown that the adhesive yield strength is singularly the most

important factor in these type of joints, while other factors, namely

the joint E/D ratio, adhesive thickness, and adhesive hardening slope

were found to be the other significant factors influencing load

sharing (D was the bolt diameter and E represented the distance

between the free end of the substrate to bolt centerline). Additionally,

studies show that the use of metal inserts in the bolt tension

relaxation is minimized and the joint efficiency is increased in terms

of joint stiffness and strength by using metal inserts in fiber

reinforced composite bolted joints structures. The use of material

nonlinearity on load distribution in multi-bolt composite joints

showed that increasing the degree of material nonlinearity of the

members causes a decrease and an increase in the amount of the load

transferred by the inner and outer bolts of the joint, respectively. The

study of lateral displacement of the grip on single lap composite-to-

aluminum bolted joints showed that the influence of lateral

displacement of the grip of the joint results in 13 % smaller joint

stiffness than the traditional model, causing a delay in failure load of

the joint due to lateral displacement of the grip. However, the study

on the effects of pin hole geometry, adherend thickness and joint

type, showed that increasing the adherend thickness improves the

joint performance in composite single lap joints as well as in scarf

joints. Additionally, taper in single lap joints provided a significant

advantage over the simple single lap joints in terms of axial tensile

strength. According to a detailed finite element investigation on a

single lap carbon fiber reinforced plastic composite bolted joints with

countersunk fasteners under static load five different stages were

identified in the joint behavior: (i) no-slip, (ii) slip, (iii) full contact,

(iv) damage and (v) final Failure. Studies performed on the bolted

carbon/epoxy composite π joints showed a larger load carrying

capability with a massive weight reduction compared to its

aluminum counterpart. Additionally, the bolted composite π joint

and its aluminum counterpart showed that the bolted composite π

joint exhibits a larger load carrying capability with a considerable

weight reduction. Furthermore, it was shown that any increase in the

bolt-hole clearance leads to an increase in bolt rotation, as well as a

decrease in bolt-hole contact area, and hence, a reduction in joint

stiffness.

References:

[1] D. M. Gleich, Stress analysis of structural bonded joints,

Delft University Press, 2002, pp. 122.

[2] M. Shishesaz, M. M. Attar, H. Robati, The Effect of

Fiber Arrangement on Stress Concentration Around a

Pin in a Laminated Composite Joint, in ASME, 10th

Biennial Conference on Engineering Systems Design

and Analysis ESDA2010-24587, 2010, pp. 153-161.

[3] S. Zhou, Z. Wang, J. Zhou, X. Wu, Experimental and

numerical investigation on bolted composite joint made

by vacuum assisted resin injection, Composites Part B:

Engineering, Vol. 45, pp. 1620-1628, 2013.

[4] Load Development and Automation for Composite

Bolted Joint Bearing and Bypass Analysis, 2010

(American Institute of Aeronautics and Astronautics).

[5] M. Keikhosravy, R. Hashemi Oskouei, P. Soltani, A.

Atas, C. Soutis, Effect of geometric parameters on the

stress distribution in Al 2024-T3 single-lap bolted joints,

International Journal of Structural Integrity, Vol. 3, No.

1, pp. 79-93, 2012.

[6] W.-H. Chen, S.-S. Lee, J.-T. Yeh, Three-dimensional

contact stress analysis of a composite laminate with

bolted joint, Composite Structures, Vol. 30, pp. 287-

297, 1995.

[7] T. J. Whitney, E. V. Iarve, R. A. Brockman, Singular

stress fields near contact boundaries in a composite

bolted joint, International Journal of Solids and

Structures, Vol. 41, pp. 1893-1909, 2004.

[8] F. Ascione, A preliminary numerical and experimental

investigation on the shear stress distribution on multi-

row bolted FRP joints, Mechanics Research

Communications, Vol. 37, No. 2, pp. 164-168,

2010/03/01/, 2010.

[9] M. H. Ahmad, Stress distribution in composite double-

lap bolted joints incorporating with clamp-up, Applied

Mechanics and Materials, Vol. 660, pp. 152-156, 2014.

[10] Analysis of a Preloaded Bolted Joint in a Ceramic

Composite Combustor, 2003 (American Institute of

Aeronautics and Astronautics).

[11] M. P. Cavatorta, D. S. Paolino, L. Peroni, M. Rodino, A

finite element simulation and experimental validation of

a composite bolted joint loaded in bending and torsion,

Composites Part A: Applied Science and

Manufacturing, Vol. 38, pp. 1251-1261, 2007.

[12] An experimental investigation of composite bonded

and/or bolted repairs using single lap joint designs,

1997 (American Institute of Aeronautics and

Astronautics).

[13] An Analytical Method for Evaluating Bolted Joint

Repairs in Composite Structures, 2011 (American

Institute of Aeronautics and Astronautics).

[14] A. Vander Klok, A. Dutta, S. A. Tekalur, Metal to

composite bolted joint behavior evaluated at impact

rates of loading, Composite Structures, Vol. 106, pp.

446-452, 2013.

[15] P. P. Camanho, C. M. L. Tavares, R. de Oliveira, A. T.

Marques, A. J. M. Ferreira, Increasing the efficiency of

composite single-shear lap joints using bonded inserts,

Composites Part B: Engineering, Vol. 36, pp. 372-383,

2005.

[16] A. M. Girão Coelho, J. T. Mottram, A review of the

behaviour and analysis of bolted connections and joints

in pultruded fibre reinforced polymers, Materials &

Design, Vol. 74, pp. 86-107, 2015/06/05/, 2015.

[17] C. T. McCarthy, P. J. Gray, An analytical model for the

prediction of load distribution in highly torqued multi-

bolt composite joints, Composite Structures, Vol. 93,

No. 2, pp. 287-298, 2011/01/01/, 2011.

[18] K. Bodjona, K. Raju, G.-H. Lim, L. Lessard, Load

sharing in single-lap bonded/bolted composite joints.

Part I: Model development and validation, Composite

Structures, Vol. 129, pp. 268-275, 2015.

[19] K. Bodjona, L. Lessard, Load sharing in single-lap

bonded/bolted composite joints. Part II: Global

sensitivity analysis, Composite Structures, Vol. 129, pp.

276-283, 2015.

[20] K. P. Raju, K. Bodjona, G.-H. Lim, L. Lessard,

Improving load sharing in hybrid bonded/bolted

composite joints using an interference-fit bolt,

M. Shishesaz and M. Hosseini

424

Composite Structures, Vol. 149, pp. 329-338, 2016.

[21] V. Mara, R. Haghani, M. Al-Emrani, Improving the

performance of bolted joints in composite structures

using metal inserts, Journal of Composite Materials,

Vol. 50, No. 21, pp. 3001-3018, 2016.

[22] E. Paroissien, F. Lachaud, S. Schwartz, A. Da Veiga, P.

Barrière, Simplified stress analysis of hybrid

(bolted/bonded) joints, International Journal of

Adhesion and Adhesives, Vol. 77, pp. 183-197,

2017/09/01/, 2017.

[23] F. Taheri-Behrooz, A. R. Shamaei Kashani, R. N.

Hefzabad, Effects of material nonlinearity on load

distribution in multi-bolt composite joints, Composite

Structures, Vol. 125, pp. 195-201, 2015/07/01/, 2015.

[24] C. Santiuste, E. Barbero, M. Henar Miguélez,

Computational analysis of temperature effect in

composite bolted joints for aeronautical applications,

Journal of Reinforced Plastics and Composites, Vol. 30,

No. 1, pp. 3-11, 2011.

[25] A. Olmedo, C. Santiuste, E. Barbero, An analytical

model for the secondary bending prediction in single-lap

composite bolted-joints, Composite Structures, Vol.

111, pp. 354-361, 2014/05/01/, 2014.

[26] L. Awadhani, A. Bewoor, Behavior of single lap

composite bolted joint under traction loading:

Experimental investigation, in Proceeding of, AIP

Publishing, pp. 020124.

[27] S. W. Wang, X. Q. Cheng, X. Guo, X. Li, G. Chen,

Influence of Lateral Displacement of the Grip on Single

lap Composite-to-Aluminum Bolted Joints,

Experimental Mechanics, Vol. 56, No. 3, pp. 407-417,

March 01, 2016.

[28] J. Kratochvil, W. Becker, Structural analysis of

composite bolted joints using the complex potential

method, Composite Structures, Vol. 92, No. 10, pp.

2512-2516, 2010/09/01/, 2010.

[29] Y. Zhou, Q. Fei, Evaluation of opening-hole shapes for

rivet connection of a composite plate, Proceedings of

the Institution of Mechanical Engineers, Part C:

Journal of Mechanical Engineering Science, Vol. 231,

No. 20, pp. 3810-3817, 2017.

[30] T. Qin, L. Zhao, J. Zhang, Fastener effects on

mechanical behaviors of double-lap composite joints,

Composite Structures, Vol. 100, pp. 413-423,

2013/06/01/, 2013.

[31] I. F. Soykok, End geometry and pin-hole effects on

axially loaded adhesively bonded composite joints,

Composites Part B: Engineering, Vol. 77, pp. 129-138,

2015/08/01/, 2015.

[32] G. M. Pearce, A. F. Johnson, R. S. Thomson, D. W.

Kelly, Experimental Investigation of Dynamically

Loaded Bolted Joints in Carbon Fibre Composite

Structures, Applied Composite Materials, Vol. 17, No.

3, pp. 271-291, June 01, 2010.

[33] S. Daouk, F. Louf, C. Cluzel, O. Dorival, L.

Champaney, S. Audebert, Study of the dynamic

behavior of a bolted joint under heavy loadings, Journal

of Sound and Vibration, Vol. 392, pp. 307-324,

2017/03/31/, 2017.

[34] G. M. K. Pearce, A. F. Johnson, A. K. Hellier, R. S.

Thomson, A Stacked-Shell Finite Element Approach for

Modelling a Dynamically Loaded Composite Bolted

Joint Under in-Plane Bearing Loads, Applied Composite

Materials, Vol. 20, No. 6, pp. 1025-1039, December 01,

2013.

[35] L. Feo, G. Marra, A. S. Mosallam, Stress analysis of

multi-bolted joints for FRP pultruded composite

structures, Composite Structures, Vol. 94, No. 12, pp.

3769-3780, 2012/12/01/, 2012.

[36] Z. Shen, D. Hu, Y. Zhang, Q. Cai, X. Han, Continuous

twice-impacts analysis of UHMWPE laminate fixed

with bolted joints, International Journal of Impact

Engineering, Vol. 109, pp. 293-301, 2017/11/01/, 2017.

[37] M. Y. Tsai, J. Morton, An investigation into the stresses

in double-lap adhesive joints with laminated composite

adherends, International Journal of Solids and

Structures, Vol. 47, pp. 3317-3325, 2010.

[38] M. Y. Tsai, J. Morton, F. L. Matthews, Experimental

and Numerical Studies of a Laminated Composite

Single-Lap Adhesive Joint, Journal of Composite

Materials, Vol. 29, pp. 1254-1275, 1995.

[39] Q. M. Li, R. A. W. Mines, R. S. Birch, Static and

dynamic behaviour of composite riveted joints in

tension, International Journal of Mechanical Sciences,

Vol. 43, pp. 1591-1610, 2001.

[40] S. W. Lee, D. G. Lee, K. S. Jeong, Static and Dynamic

Torque Characteristics of Composite Cocured Single

Lap Joint, Journal of Composite Materials, Vol. 31, pp.

2188-2201, 1997.

[41] C. Stocchi, P. Robinson, S. T. Pinho, A detailed finite

element investigation of composite bolted joints with

countersunk fasteners, Composites Part A: Applied

Science and Manufacturing, Vol. 52, pp. 143-150,

2013/09/01/, 2013.

[42] B. Mandal, A. Chakrabarti, A simple homogenization

scheme for 3D finite element analysis of composite

bolted joints, Composite Structures, Vol. 120, pp. 1-9,

2015/02/01/, 2015.

[43] H.-T. Thai, B. Uy, Finite element modelling of blind

bolted composite joints, Journal of Constructional Steel

Research, Vol. 112, pp. 339-353, 2015/09/01/, 2015.

[44] N. M. Chowdhury, W. K. Chiu, J. Wang, P. Chang,

Experimental and finite element studies of bolted,

bonded and hybrid step lap joints of thick carbon

fibre/epoxy panels used in aircraft structures,

Composites Part B: Engineering, Vol. 100, pp. 68-77,

2016/09/01/, 2016.

[45] L. Prabhu, V. Krishnaraj, S. Sathish, V. Sathyamoorthy,

Experimental and Finite Element Analysis of GFRP

Composite Laminates with Combined Bolted and

Bonded Joints, Indian Journal of Science and

Technology, Vol. 10, No. 14, 2017.

[46] P. J. Gray, C. T. McCarthy, A highly efficient user-

defined finite element for load distribution analysis of

large-scale bolted composite structures, Composites

Science and Technology, Vol. 71, No. 12, pp. 1517-

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

425

1527, 2011/08/19/, 2011.

[47] P. J. Gray, C. T. McCarthy, A global bolted joint model

for finite element analysis of load distributions in multi-

bolt composite joints, Composites Part B: Engineering,

Vol. 41, pp. 317-325, 2010.

[48] L. Zhou, D. Zhang, L. Zhao, X. Zhou, J. Zhang, F. Liu,

Design and analysis of a novel bolted composite π joint

under bending load, Materials & Design, Vol. 98, pp.

201-208, 2016/05/15/, 2016.

[49] X. Cheng, J. Fan, S. Liu, X. Guo, Y. Xu, T. Zhang,

Design and investigation of composite bolted π-joints

with an unconventional configuration under bending

load, Composites Part B: Engineering, Vol. 85, pp. 59-

67, 2016/02/01/, 2016.

[50] P. Lopez-Cruz, J. Laliberté, L. Lessard, Investigation of

bolted/bonded composite joint behaviour using design

of experiments, Composite Structures, Vol. 170, pp.

192-201, 2017/06/15/, 2017.

[51] A. Vassilopoulos, 2014, Fatigue and fracture of

adhesively-bonded composite joints, Elsevier,

[52] T. Ireman, Three-dimensional stress analysis of bolted

single-lap composite joints, Composite Structures, Vol.

43, No. 3, pp. 195-216, 1998/11/01/, 1998.

[53] K. I. Tserpes, G. Labeas, P. Papanikos, T. Kermanidis,

Strength prediction of bolted joints in graphite/epoxy

composite laminates, Composites Part B: Engineering,

Vol. 33, No. 7, pp. 521-529, 2002/10/01/, 2002.

[54] Y. Xiao, T. Ishikawa, Bearing strength and failure

behavior of bolted composite joints (part I:

Experimental investigation), Composites Science and

Technology, Vol. 65, No. 7, pp. 1022-1031,

2005/06/01/, 2005.

[55] Y. Xiao, T. Ishikawa, Bearing strength and failure

behavior of bolted composite joints (part II: modeling

and simulation), Composites Science and Technology,

Vol. 65, No. 7, pp. 1032-1043, 2005/06/01/, 2005.

[56] P. A. Sharos, B. Egan, C. T. McCarthy, An analytical

model for strength prediction in multi-bolt composite

joints at various loading rates, Composite Structures,

Vol. 116, pp. 300-310, 2014/09/01/, 2014.

[57] M. A. McCarthy, C. T. McCarthy, V. P. Lawlor, W. F.

Stanley, Three-dimensional finite element analysis of

single-bolt, single-lap composite bolted joints: part I—

model development and validation, Composite

Structures, Vol. 71, pp. 140-158, 2005.

[58] C. T. McCarthy, M. A. McCarthy, Three-dimensional

finite element analysis of single-bolt, single-lap

composite bolted joints: Part II––effects of bolt-hole

clearance, Composite Structures, Vol. 71, pp. 159-175,

2005.

[59] P. J. Gray, C. T. McCarthy, An analytical model for the

prediction of through-thickness stiffness in tension-

loaded composite bolted joints, Composite Structures,

Vol. 94, No. 8, pp. 2450-2459, 2012/07/01/, 2012.

[60] M. El Zaroug, F. Kadioglu, M. Demiral, D. Saad,

Experimental and numerical investigation into strength

of bolted, bonded and hybrid single lap joints: Effects of

adherend material type and thickness, International

Journal of Adhesion and Adhesives, Vol. 87, pp. 130-

141, 2018/12/01/, 2018.

[61] L. Zhao, M. Shan, F. Liu, J. Zhang, A probabilistic

model for strength analysis of composite double-lap

single-bolt joints, Composite Structures, Vol. 161, pp.

419-427, 2017/02/01/, 2017.

[62] H.-L. Ma, Z. Jia, K.-t. Lau, X. Li, D. Hui, S.-q. Shi,

Enhancement on mechanical strength of adhesively-

bonded composite lap joints at cryogenic environment

using coiled carbon nanotubes, Composites Part B:

Engineering, Vol. 110, pp. 396-401, 2017/02/01/, 2017.

[63] A. Othman, K. J. Jadee, M.-Z. Ismadi, Mitigating stress

concentration through defense hole system for

improvement in bearing strength of composite bolted

joint, Part 1: Numerical analysis, Journal of Composite

Materials, Vol. 51, No. 26, pp. 3685-3699, 2017.

[64] H. Li, Z. Lu, Y. Zhang, Probabilistic strength analysis

of bolted joints in laminated composites using point

estimate method, Composite Structures, Vol. 88, No. 2,

pp. 202-211, 2009/04/01/, 2009.

[65] J. H. Choi, Y. H. Lee, J. H. Kweon, W. S. Che, Strength

of Composite Laminated Bolted Joint Subjected to a

Clamping Force, Key Engineering Materials, Trans

Tech Publ, 2006, pp. 1777-1780.

[66] H.-S. Chen, The static and fatigue strength of bolted

joints in composites with hygrothermal cycling,

Composite Structures, Vol. 52, No. 3, pp. 295-306,

2001/05/01/, 2001.

[67] Y. Ling, An estimation method of bearing strength of

bolted joints in fibre reinforced composite, Applied

Mathematics and Mechanics, Vol. 7, No. 1, pp. 103-

109, January 01, 1986.

[68] Y. Pekbey, The bearing strength and failure behavior of

bolted e-glass/epoxy composite joints, Mechanics of

Composite Materials, Vol. 44, No. 4, pp. 397-414, July

01, 2008.

[69] T. Katsumata, Y. Mizutani, A. Todoroki, R. Matsuzaki,

Study of high-strength CFRP bolted joints with failure-

monitoring cone washers, Frontiers of Mechanical

Engineering, Vol. 6, No. 3, pp. 272, August 20, 2011.

[70] T. Collings, 1977, The strength of bolted joints in multi-

directional CFRP laminates, Citeseer,

[71] G. Kretsis, F. L. Matthews, The strength of bolted joints

in glass fibre/epoxy laminates, Composites, Vol. 16, No.

2, pp. 92-102, 1985/04/01/, 1985.

[72] H. Ahmad, A. D. Crocombe, P. A. Smith, Strength

prediction in CFRP woven laminate bolted double-lap

joints under quasi-static loading using XFEM,

Composites Part A Applied Science and Manufacturing,

Vol. 56, pp. 192–202, 2014.

[73] A. Ataş, C. Soutis, Strength prediction of bolted joints

in CFRP composite laminates using cohesive zone

elements, Composites Part B: Engineering, Vol. 58, pp.

25-34, 2014.

[74] F. Esmaeili, M. Zehsaz, T. N. Chakherlou, Experimental

Investigations on the Effects of Torque Tightening on

the Fatigue Strength of Double-lap Simple Bolted and

Hybrid (Bolted/Bonded) Joints, Strain, Vol. 50, No. 4,

M. Shishesaz and M. Hosseini

426

pp. 347-354, 2014.

[75] O. Sayman, R. Siyahkoc, F. Sen, R. Ozcan,

Experimental Determination of Bearing Strength in

Fiber Reinforced Laminated Composite Bolted Joints

under Preload, Journal of Reinforced Plastics and

Composites, Vol. 26, No. 10, pp. 1051-1063, 2007.

[76] P. D. Herrington, M. Sabbaghian, Effect of Radial

Clearance between Bolt and Washer on the Bearing

Strength of Composite Bolted Joints, Journal of

Composite Materials, Vol. 26, No. 12, pp. 1826-1843,

1992.

[77] F. Esmaeili, M. Zehsaz, T. N. Chakherlou, S.

Hasanifard, Experimental and Numerical Study of the

Fatigue Strength of Double Lap Bolted Joints and the

Effect of Torque Tightening on the Fatigue Life of

Jointed Plates, Transactions of the Indian Institute of

Metals, Vol. 67, No. 4, pp. 581-588, August 01, 2014.

[78] H. Ahmad, A. D. Crocombe, P. A. Smith, Strength

prediction in CFRP woven laminate bolted single-lap

joints under quasi-static loading using XFEM,

Composites Part A: Applied Science and

Manufacturing, Vol. 66, pp. 82-93, 2014/11/01/, 2014.

[79] L. Liu, J. Zhang, K. Chen, H. Wang, Influences of

assembly parameters on the strength of bolted

composite-metal joints under tensile loading, Advanced

Composite Materials, Vol. 22, No. 5, pp. 339-359,

2013/10/01, 2013.

[80] J. H. Walter, R. R. Schmitt, Influence of Clamp-Up

Force on the Strength of Bolted Composite Joints, AIAA

Journal, Vol. 32, No. 3, pp. 665-667, 1994/03/01, 1994.

[81] F. X. Irisarri, F. Laurin, N. Carrere, 6 - Strength

prediction of bolted joints in carbon fibre reinforced

polymer (CFRP) composites, in: P. Camanho, L. Tong,

Composite Joints and Connections, Eds., pp. 208-244:

Woodhead Publishing, 2011.

[82] S. Nilsson, Increasing Strength of Graphite/Epoxy

Bolted Joints by Introducing an Adhesively Bonded

Metallic Insert, Journal of Composite Materials, Vol.

23, No. 7, pp. 642-650, 1989.

[83] F. Gamdani, R. Boukhili, A. Vadean, Tensile strength of

open-hole, pin-loaded and multi-bolted single-lap joints

in woven composite plates, Materials & Design, Vol.

88, pp. 702-712, 2015/12/25/, 2015.

[84] H. Ahmad, M. A. Abed, Strength Prediction of Double-

Lap Bolted Joints of Woven Fabric CFRP Composite

Plates Using Hashin Formulations, in Proceeding of,

Trans Tech Publ, pp. 290-294.

[85] F. Nerilli, G. Vairo, Progressive damage in composite

bolted joints via a computational micromechanical

approach, Composites Part B: Engineering, Vol. 111,

pp. 357-371, 2017/02/15/, 2017.

[86] H. Yazdani Nezhad, B. Egan, F. Merwick, C. T.

McCarthy, Bearing damage characteristics of fibre-

reinforced countersunk composite bolted joints

subjected to quasi-static shear loading, Composite

Structures, Vol. 166, pp. 184-192, 2017/04/15/, 2017.

[87] B. He, D. Ge, Coupled continuum damage mechanics

and failure envelope method for failure prediction of

composite multi-bolt joints, Journal of Reinforced

Plastics and Composites, Vol. 36, No. 8, pp. 563-578,

2017.

[88] Y. Zhou, H. Yazdani Nezhad, C. Hou, X. Wan, C. T.

McCarthy, M. A. McCarthy, A three dimensional

implicit finite element damage model and its application

to single-lap multi-bolt composite joints with variable

clearance, Composite Structures, Vol. 131, pp. 1060-

1072, 2015/11/01/, 2015.

[89] A. Du, Y. Liu, H. Xin, Y. Zuo, Progressive damage

analysis of PFRP double-lap bolted joints using explicit

finite element method, Composite Structures, Vol. 152,

pp. 860-869, 2016/09/15/, 2016.

[90] C. Hühne, A. K. Zerbst, G. Kuhlmann, C. Steenbock, R.

Rolfes, Progressive damage analysis of composite

bolted joints with liquid shim layers using constant and

continuous degradation models, Composite Structures,

Vol. 92, No. 2, pp. 189-200, 2010/01/01/, 2010.

[91] J. Zhang, F. Liu, L. Zhao, Y. Chen, B. Fei, A progressive

damage analysis based characteristic length method for

multi-bolt composite joints, Composite Structures, Vol.

108, pp. 915-923, 2014/02/01/, 2014.

[92] G. Kolks, K. I. Tserpes, Efficient progressive damage

modeling of hybrid composite/titanium bolted joints,

Composites Part A: Applied Science and

Manufacturing, Vol. 56, pp. 51-63, 2014/01/01/, 2014.

[93] M. Chishti, C. H. Wang, R. S. Thomson, A. C. Orifici,

Experimental investigation of damage progression and

strength of countersunk composite joints, Composite

Structures, Vol. 94, No. 3, pp. 865-873, 2012/02/01/,

2012.

[94] Y. Zhou, H. Yazdani-Nezhad, M. A. McCarthy, X.

Wan, C. McCarthy, A study of intra-laminar damage in

double-lap, multi-bolt, composite joints with variable

clearance using continuum damage mechanics,

Composite Structures, Vol. 116, pp. 441-452,

2014/09/01/, 2014.

[95] G. Lampeas, N. Perogamvros, Analysis of composite

bolted joints by a macro-modelling approach,

International Journal of Structural Integrity, Vol. 7, No.

3, pp. 412-428, 2016.

[96] A. Ataş, C. Soutis, Subcritical damage mechanisms of

bolted joints in CFRP composite laminates, Composites

Part B: Engineering, Vol. 54, pp. 20-27, 2013/11/01/,

2013.

[97] L. V. Awadhani, A. K. Bewoor, Analytical and

experimental investigation of Effect of geometric

parameters on the failure modes in a single lap single

bolted metal to GFRP composite bolted joints subjected

to axial tensile loading, Materials Today: Proceedings,

Vol. 4, No. 8, pp. 7345-7350, 2017/01/01/, 2017.

[98] X. F. Hu, A. Haris, M. Ridha, V. B. C. Tan, T. E. Tay,

Progressive failure of bolted single-lap joints of woven

fibre-reinforced composites, Composite Structures, Vol.

189, pp. 443-454, 2018/04/01/, 2018.

[99] X. Cheng, S. Wang, J. Zhang, W. Huang, Y. Cheng, J.

Zhang, Effect of damage on failure mode of multi-bolt

composite joints using failure envelope method,

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

427

Composite Structures, Vol. 160, pp. 8-15, 2017/01/15/,

2017.

[100] K. C. Warren, R. A. Lopez-Anido, S. S. Vel, H. H.

Bayraktar, Progressive failure analysis of three-

dimensional woven carbon composites in single-bolt,

double-shear bearing, Composites Part B: Engineering,

Vol. 84, pp. 266-276, 2016/01/01/, 2016.

[101] Z. Kapidžić, H. Ansell, J. Schön, K. Simonsson, Quasi-

static bearing failure of CFRP composite in biaxially

loaded bolted joints, Composite Structures, Vol. 125,

pp. 60-71, 2015/07/01/, 2015.

[102] P. Liu, X. Cheng, S. Wang, S. Liu, Y. Cheng, Numerical

analysis of bearing failure in countersunk composite

joints using 3D explicit simulation method, Composite

Structures, Vol. 138, pp. 30-39, 2016/03/15/, 2016.

[103] F. Nerilli, M. Marino, G. Vairo, A Numerical Failure

Analysis of Multi-bolted Joints in FRP Laminates Based

on Basalt Fibers, Procedia Engineering, Vol. 109, pp.

492-506, 2015/01/01/, 2015.

[104] M. Ozen, O. Sayman, Failure loads of mechanical

fastened pinned and bolted composite joints with two

serial holes, Composites Part B: Engineering, Vol. 42,

No. 2, pp. 264-274, 2011/03/01/, 2011.

[105] U. A. Khashaba, T. A. Sebaey, K. A. Alnefaie, Failure

and reliability analysis of pinned-joints composite

laminates: Effects of stacking sequences, Composites

Part B: Engineering, Vol. 45, No. 1, pp. 1694-1703,

2013/02/01/, 2013.

[106] U. Khashaba, T. Sebaey, K. Alnefaie, Failure and

reliability analysis of pinned-joint composite laminates:

Effects of pin–hole clearance, Journal of Composite

Materials, Vol. 47, No. 18, pp. 2287-2298, 2013.

[107] Z. Wang, S. Zhou, J. Zhang, X. Wu, L. Zhou,

Progressive failure analysis of bolted single-lap

composite joint based on extended finite element

method, Materials & Design, Vol. 37, pp. 582-588,

2012.

[108] F. Liu, L. Zhao, S. Mehmood, J. Zhang, B. Fei, A

modified failure envelope method for failure prediction

of multi-bolt composite joints, Composites Science and

Technology, Vol. 83, pp. 54-63, 2013/06/28/, 2013.

[109] I. F. Soykok, O. Sayman, M. Ozen, B. Korkmaz, Failure

analysis of mechanically fastened glass fiber/epoxy

composite joints under thermal effects, Composites Part

B: Engineering, Vol. 45, No. 1, pp. 192-199,

2013/02/01/, 2013.

[110] A. Ataş, G. F. Mohamed, C. Soutis, Progressive failure

analysis of bolted joints in composite laminates,

Plastics, Rubber and Composites, Vol. 41, No. 4-5, pp.

209-214, 2012/06/01, 2012.

[111] F. Lu, D. a. Cai, J. Tang, W. Li, J. Deng, G. Zhou,

Bearing failure of single-/double-shear composite

bolted joints: An explicit finite element modeling,

Journal of Reinforced Plastics and Composites, Vol. 37,

No. 14, pp. 933-944, 2018.

[112] S. Y. Lee, H. Ahmad, Bearing Stress at Failure of

Double-Lap Hybrid Joints in Woven Fabric Kenaf Fiber

Composite Plates under Quasi-static Loading, MATEC

Web Conf., Vol. 103, pp. 02008, 2017.

[113] L. Zhao, T. Qin, J. Zhang, M. Shan, B. Fei,

Determination method of stress concentration relief

factors for failure prediction of composite multi-bolt

joints, Journal of Composite Materials, Vol. 49, No. 14,

pp. 1667-1680, 2015.

[114] J. Zhang, F. Liu, L. Zhao, J. Zhi, L. Zhou, B. Fei,

Influence of end distances on the failure of composite

bolted joints, Journal of Reinforced Plastics and

Composites, Vol. 34, No. 5, pp. 388-404, 2015.

[115] Á. Olmedo, C. Santiuste, On the prediction of bolted

single-lap composite joints, Composite Structures, Vol.

94, No. 6, pp. 2110-2117, 2012/05/01/, 2012.

[116] J. Fan, X. Cheng, S. Wang, X. Guo, T. Zhang,

Experimental and numerical investigation of composite

bolted π-joint subjected to bending load, Composites

Part B: Engineering, Vol. 78, pp. 324-330, 2015/09/01/,

2015.

[117] M.-G. Ko, J.-H. Kweon, J.-H. Choi, Fatigue

characteristics of jagged pin-reinforced composite

single-lap joints in hygrothermal environments,

Composite Structures, Vol. 119, pp. 59-66, 2015/01/01/,

2015.

[118] I. K. Giannopoulos, D. Doroni-Dawes, K. I. Kourousis,

M. Yasaee, Effects of bolt torque tightening on the

strength and fatigue life of airframe FRP laminate bolted

joints, Composites Part B: Engineering, Vol. 125, pp.

19-26, 2017/09/15/, 2017.

[119] Y. Sun, G. Z. Voyiadjis, W. Hu, F. Shen, Q. Meng,

Fatigue and fretting fatigue life prediction of double-lap

bolted joints using continuum damage mechanics-based

approach, International Journal of Damage Mechanics,

Vol. 26, No. 1, pp. 162-188, 2017.

[120] G. Scarselli, E. Castorini, F. W. Panella, R. Nobile, A.

Maffezzoli, Structural behaviour modelling of bolted

joints in composite laminates subjected to cyclic

loading, Aerospace Science and Technology, Vol. 43,

pp. 89-95, 2015/06/01/, 2015.

[121] S. Zhou, Y. Sun, J. Ge, X. Chen, Multiaxial fatigue life

prediction of composite bolted joint under constant

amplitude cycle loading, Composites Part B:

Engineering, Vol. 74, pp. 131-137, 2015/06/01/, 2015.

[122] Z. Kapidžić, H. Ansell, J. Schön, K. Simonsson, Fatigue

bearing failure of CFRP composite in biaxially loaded

bolted joints at elevated temperature, Composite

Structures, Vol. 127, pp. 298-307, 2015/09/01/, 2015.

[123] J. Wang, N. Zhang, S. Guo, Experimental and numerical

analysis of blind bolted moment joints to CFTST

columns, Thin-Walled Structures, Vol. 109, pp. 185-

201, 2016/12/01/, 2016.

[124] S. Heimbs, S. Schmeer, J. Blaurock, S. Steeger, Static

and dynamic failure behaviour of bolted joints in carbon

fibre composites, Composites Part A: Applied Science

and Manufacturing, Vol. 47, pp. 91-101, 2013/04/01/,

2013.

[125] J. Zhang, F. Liu, L. Zhao, B. Fei, A novel characteristic

curve for failure prediction of multi-bolt composite

joints, Composite Structures, Vol. 108, pp. 129-136,

M. Shishesaz and M. Hosseini

428

2014/02/01/, 2014.

[126] G. M. K. Pearce, A. F. Johnson, A. K. Hellier, R. S.

Thomson, A study of dynamic pull-through failure of

composite bolted joints using the stacked-shell finite

element approach, Composite Structures, Vol. 118, pp.

86-93, 2014/12/01/, 2014.

[127] A. Fontanelli, P. Diaz Montiel, S. Venkataraman,

Bearing Failure Predictions of Composite Bolted Joints

using Continuum Damage Models, AIAA SciTech

Forum in: 2018 AIAA/ASCE/AHS/ASC Structures,

Structural Dynamics, and Materials Conference, Eds.:

American Institute of Aeronautics and Astronautics,

2018.

[128] F. Sen, M. Pakdil, O. Sayman, S. Benli, Experimental

Failure Analysis of Glass-Epoxy Laminated Composite

Bolted-Joints with Clearance Under Preload,

International Journal of Damage Mechanics, Vol. 20,

No. 2, pp. 163-178, 2011.

[129] W. J. Paulson, C. Oskay, Failure Prediction of

Countersunk Composite Bolted Joints Using Reduced

Order Multiple Space-Time Homogenization, in

Proceeding of.

[130] A. P. K. Joseph, P. Davidson, A. M. Waas, Intra-inter

Crack Band Model (I2CBM) for Progressive Damage

and Failure Analysis of Joints, AIAA SciTech Forum

in: 58th AIAA/ASCE/AHS/ASC Structures, Structural

Dynamics, and Materials Conference, Eds.: American

Institute of Aeronautics and Astronautics, 2017.

[131] B. Mandal, A. Chakrabarti, Numerical failure

assessment of multi-bolt FRP composite joints with

varying sizes and preloads of bolts, Composite

Structures, Vol. 187, pp. 169-178, 2018/03/01/, 2018.

[132] J. B. Bai, R. A. Shenoi, X. Y. Yun, J. J. Xiong,

Progressive damage modelling of hybrid RTM-made

composite Π-joint under four-point flexure using mixed

failure criteria, Composite Structures, Vol. 159, pp. 327-

334, 2017/01/01/, 2017.

[133] J. H. Stockdale, F. L. Matthews, The effect of clamping

pressure on bolt bearing loads in glass fibre-reinforced

plastics, Composites, Vol. 7, No. 1, pp. 34-38,

1976/01/01/, 1976.

[134] T. Sawa, T. Kobayashi, The Strength of Joints

Combining an Adhesive with a Bolt, The Journal of

Adhesion, Vol. 25, No. 4, pp. 269-280, 1988/06/01,

1988.

[135] L. Yao, Q. Feng, D. Wan, L. Wu, K. Yang, J. Hou, B.

Liu, Q. Wan, Experiment and finite element simulation

of high strength steel adhesive joint reinforced by rivet

for automotive applications, Journal of Adhesion

Science and Technology, Vol. 31, No. 14, pp. 1617-

1625, 2017/07/18, 2017.

[136] M. Y. Solmaz, T. Topkaya, Progressive Failure Analysis

in Adhesively, Riveted, and Hybrid Bonded Double-

Lap Joints, The Journal of Adhesion, Vol. 89, No. 11,

pp. 822-836, 2013/11/02, 2013.

[137] G. Marannano, B. Zuccarello, Static strength and fatigue

life of optimized hybrid single lap aluminum–CFRP

structural joints, The Journal of Adhesion, Vol. 94, No.

7, pp. 501-528, 2018/06/07, 2018.

[138] G. Qin, J. Na, W. Tan, W. Mu, J. Ji, Failure prediction

of adhesively bonded CFRP-Aluminum alloy joints

using cohesive zone model with consideration of

temperature effect, The Journal of Adhesion, pp. 1-24,

2018.

[139] T. Tannert, H. Zhu, S. Myslicki, F. Walther, T. Vallée,

Tensile and fatigue investigations of timber joints with

glued-in FRP rods, The Journal of Adhesion, Vol. 93,

No. 11, pp. 926-942, 2017/09/19, 2017.

[140] A. M. Pereira, P. N. B. Reis, J. A. M. Ferreira, Effect of

the mean stress on the fatigue behaviour of single lap

joints, The Journal of Adhesion, Vol. 93, No. 6, pp. 504-

513, 2017/05/12, 2017.

[141] S. O. Olajide, E. Kandare, A. A. Khatibi, Fatigue life

uncertainty of adhesively bonded composite scarf joints

– an airworthiness perspective, The Journal of

Adhesion, Vol. 93, No. 7, pp. 515-530, 2017/06/07,

2017.

[142] T. Vallée, T. Tannert, S. Fecht, Adhesively bonded

connections in the context of timber engineering – A

Review, The Journal of Adhesion, Vol. 93, No. 4, pp.

257-287, 2017/03/21, 2017.

[143] E. W. Godwin, F. L. Matthews, A review of the strength

of joints in fibre-reinforced plastics: Part 1.

Mechanically fastened joints, Composites, Vol. 11, pp.

155-160, 1980.

[144] B. L. Agarwal, Static Strength Prediction of Bolted Joint

in Composite Material, AIAA Journal, Vol. 18, pp.

1371-1375, 1980.

[145] W.-H. Lin, M.-H. R. Jen, The Strength of Bolted and

Bonded Single-Lapped Composite Joints in Tension,

Journal of Composite Materials, Vol. 33, pp. 640-666,

1999.

[146] P. A. Smith, K. J. Pascoe, C. Polak, D. O. Stroud, The

behaviour of single-lap bolted joints in CFRP laminates,

Composite Structures, Vol. 6, pp. 41-55, 1986.

[147] T. N. Chakherlou, M. J. Razavi, A. B. Aghdam, B.

Abazadeh, An experimental investigation of the bolt

clamping force and friction effect on the fatigue

behavior of aluminum alloy 2024-T3 double shear lap

joint, Materials & Design, Vol. 32, pp. 4641-4649,

2011.

[148] F. Esmaeili, M. Zehsaz, T. N. Chakherlou, Investigation

the effect of tightening torque on the fatigue strength of

double lap simple bolted and hybrid (bolted–bonded)

joints using volumetric method, Materials & Design,

Vol. 63, pp. 349-359, 2014.

[149] J. M. Mínguez, J. Vogwell, Effect of torque tightening

on the fatigue strength of bolted joints, Engineering

Failure Analysis, Vol. 13, pp. 1410-1421, 2006.

[150] D. S. Saunders, S. C. Galea, G. K. Deirmendjian, The

development of fatigue damage around fastener holes in

thick graphite/epoxy composite laminates, Composites,

Vol. 24, pp. 309-321, 1993.

[151] B. Benchekchou, R. G. White, Stresses around fasteners

in composite structures in flexure and effects on fatigue

damage initiation part 1: cheese-head bolts, Composite

Journal of Computational Applied Mechanics, Vol. 49,No. 2, December 2018

429

Structures, Vol. 33, pp. 95-108, 1995.

[152] B. Benchekchou, R. G. White, Stresses around fasteners

in composite structures in flexure and effects on fatigue

damage initiation part 2: countersunk bolts, Composite

Structures, Vol. 33, pp. 109-119, 1995.

[153] E. Persson, I. Eriksson, P. Hammersberg, Propagation

of Hole Machining Defects in Pin-Loaded Composite

Laminates, Journal of Composite Materials, Vol. 31, pp.

383-408, 1997.

[154] E. Persson, I. Eriksson, L. Zackrisson, Effects of hole

machining defects on strength and fatigue life of

composite laminates, Composites Part A: Applied

Science and Manufacturing, Vol. 28, pp. 141-151, 1997.

[155] W. Li, H. Cai, C. Li, K. Wang, L. Fang, Micro-

mechanics of failure for fatigue strength prediction of

bolted joint structures of carbon fiber reinforced

polymer composite, Composite Structures, Vol. 124, pp.

345-356, 2015.

[156] Experimental investigation of fatigue behaviour in

composite bolted joints, 1999.

[157] A. Lanciotti, L. Lazzeri, M. Raggi, Fatigue behaviour of

mechanically fastened joints in composite materials,

Composite Structures, Vol. 33, pp. 87-94, 1995.

[158] R. Starikov, J. Schön, Local fatigue behaviour of CFRP

bolted joints, Composites Science and Technology, Vol.

62, pp. 243-253, 2002.

[159] R. Starikov, Fatigue behaviour of mechanically fastened

aluminium joints tested in spectrum loading,

International Journal of Fatigue, Vol. 26, pp. 1115-

1127, 2004.

[160] R. Starikov, J. Schön, Quasi-static behaviour of

composite joints with protruding-head bolts, Composite

Structures, Vol. 51, pp. 411-425, 2001.

[161] P. A. Smith, K. J. Pascoe, Fatigue of bolted joints in

(0/90) CFRP laminates, Composites Science and

Technology, Vol. 29, pp. 45-69, 1987.

[162] R. Starikov, J. Schön, Fatigue resistance of composite

joints with countersunk composite and metal fasteners,

International Journal of Fatigue, Vol. 24, pp. 39-47,

2002.

[163] R. Starikov, J. Schön, Experimental study on fatigue

resistance of composite joints with protruding-head

bolts, Composite Structures, Vol. 55, pp. 1-11, 2002.

[164] E. Persson, I. Eriksson, Fatigue of multiple-row bolted

joints in carbon/epoxy laminates: ranking of factors

affecting strength and fatigue life, International Journal

of Fatigue, Vol. 21, pp. 337-353, 1999.

[165] A. M. Rubin, Common failure modes for composite

aircraft structures due to secondary loads, Composites

Engineering, Vol. 2, pp. 313-320, 1992.

[166] T. S. Lim, B. C. Kim, D. G. Lee, Fatigue characteristics

of the bolted joints for unidirectional composite

laminates, Composite Structures, Vol. 72, pp. 58-68,

2006.

[167] S. Seike, Y. Takao, W.-X. Wang, T. Matsubara, Bearing

damage evolution of a pinned joint in CFRP laminates

under repeated tensile loading, International Journal of

Fatigue, Vol. 32, pp. 72-81, 2010.

[168] D. W. Wilson, Y. Tsujimoto, On phenomenological

failure criteria for composite bolted joint analysis,

Composites Science and Technology, Vol. 26, pp. 283-

305, 1986.

[169] Z. Q. Wang, S. Zhou, J. F. Zhang, X. Q. Wang, Failure

Load Prediction of Bolted Single-Lap Composite Joint

Based on XFEM, Advanced Materials Research, Trans

Tech Publ, 2011, pp. 742-745.

[170] S. Zhou, Z. Q. Wang, J. F. Zhang, Y. G. Xie, Influence

of Ply Angle on Failure Response of Bolted Composite

Joint, Advanced Materials Research, Trans Tech Publ,

2012, pp. 7128-7132.

[171] T. Sadowski, M. Kneć, P. Golewski, Experimental

investigations and numerical modelling of steel

adhesive joints reinforced by rivets, International

Journal of Adhesion and Adhesives, Vol. 30, pp. 338-

346, 2010.

[172] M. Grassi, B. Cox, X. Zhang, Simulation of pin-

reinforced single-lap composite joints, Composites

Science and Technology, Vol. 66, pp. 1623-1638, 2006.

[173] A. Ataş, C. Soutis, Application of cohesive zone

elements in damage analysis of composites: Strength

prediction of a single-bolted joint in CFRP laminates,

International Journal of Non-Linear Mechanics, Vol.

66, pp. 96-104, 2014.